Related papers: A low rank ODE for spectral clustering stability
Spectral clustering methods are widely used for detecting clusters in networks for community detection, while a small change on the graph Laplacian matrix could bring a dramatic improvement. In this paper, we propose a dual regularized…
Spectral clustering is a celebrated algorithm that partitions objects based on pairwise similarity information. While this approach has been successfully applied to a variety of domains, it comes with limitations. The reason is that there…
Neighborhood graphs are a critical but often fragile step in spectral clustering of text embeddings. On realistic text datasets, standard $k$-NN graphs can contain many disconnected components at practical sparsity levels (small $k$),…
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…
We present a new algorithm for spectral clustering based on a column-pivoted QR factorization that may be directly used for cluster assignment or to provide an initial guess for k-means. Our algorithm is simple to implement, direct, and…
We consider a variation of the spectral sparsification problem where we are required to keep a subgraph of the original graph. Formally, given a union of two weighted graphs $G$ and $W$ and an integer $k$, we are asked to find a $k$-edge…
Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely…
The community detection problem for graphs asks one to partition the n vertices V of a graph G into k communities, or clusters, such that there are many intracluster edges and few intercluster edges. Of course this is equivalent to finding…
Spectral clustering methods are known for their ability to represent clusters of diverse shapes, densities etc. However, results of such algorithms, when applied e.g. to text documents, are hard to explain to the user, especially due to…
Clustering is a fundamental task in data analysis, and spectral clustering has been recognized as a promising approach to it. Given a graph describing the relationship between data, spectral clustering explores the underlying cluster…
Constrained clustering has been well-studied for algorithms such as $K$-means and hierarchical clustering. However, how to satisfy many constraints in these algorithmic settings has been shown to be intractable. One alternative to encode…
We consider spectral clustering algorithms for community detection under a general bipartite stochastic block model (SBM). A modern spectral clustering algorithm consists of three steps: (1) regularization of an appropriate adjacency or…
We focus on spectral clustering of unlabeled graphs and review some results on clustering methods which achieve weak or strong consistent identification in data generated by such models. We also present a new algorithm which appears to…
In this paper, we consider the soft geometric block model (SGBM) with a fixed number $k \geq 2$ of homogeneous communities in the dense regime, and we introduce a spectral clustering algorithm for community recovery on graphs generated by…
Structured sparsity is an important part of the modern statistical toolkit. We say a set of model parameters has block diagonal sparsity up to permutations if its elements can be viewed as the edges of a graph that has multiple connected…
Spanners have been shown to be a powerful tool in graph algorithms. Many spanner constructions use a certain type of clustering at their core, where each cluster has small diameter and there are relatively few spanner edges between…
Given a graph $G$ that can be partitioned into $k$ disjoint expanders with outer conductance upper bounded by $\epsilon\ll 1$, can we efficiently construct a small space data structure that allows quickly classifying vertices of $G$…
Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even…
Subspace clustering refers to the problem of segmenting a set of data points approximately drawn from a union of multiple linear subspaces. Aiming at the subspace clustering problem, various subspace clustering algorithms have been proposed…
Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow…